MGMAT digits

[rommysingh]

In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56.

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564.

[MartyMurray]

To make this thing simpler we can translate the question to "What is the value of x."

Statement 1 can be translated to "If x is rounded to the nearest hundredth, then x = 10 - 8.56 = 1.44."

This can easily be shown to be insufficient, because rounding 1.4ab5 to the nearest hundredth involves just a and b, and a could be 4 and b any digit less than 5 or a could be 3 and b could be any digit 5 or greater. Either way x would round to 1.44.

Statement 2 can be translated to "If x is rounded to the nearest thousandth, then x = 1.436."

Since the ten thousandths place of 1.4ab5 is occupied by the digit 5, we know that we will round up when rounding to the nearest thousandth. So if b rounds up to 6, then b must be 5, and so far we know that x = 1.4a55.

Meanwhile rounding to the nearest thousandth does not change the hundredths. So a must be 3 and x = 1.4355.

So using Statement 2 we can figure out the values of a, b and x, and so Statement 2 is sufficient and the answer is B.

[Brent@GMATPrepNow]

In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564

Target question: What is the value of 10 - x?

Given: X = 1.4ab5

Statement 1: If x is rounded to the nearest hundredth, then 10 - x = 8.56
10 - 1.44 = 8.56
So, x rounded to the nearest HUNDREDTH = 1.44
So, x COULD equal 1.4355, 1.4365, 1.4375, 1.4385, 1.4395, 1.4405, 1.4415, 1.4425, 1.4435 OR 1.4445
Given all of the different possible values of x, 10 - x could have MANY different values.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If x is rounded to the nearest thousandth, then 10 - x = 8.564
10 - 1.436 = 8.564
In other words, x rounded to the nearest THOUSANDTH = 1.436
This tells us that a must equal 3, leaving us with 1.43b5
If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

[rommysingh]

Thanks for the response!

I needed to know that in digit problems when you round up a number could there be a domino effect..

for e.g. 8.3xy rounded to nearest tenth will be

so if x =4 and y =7 then the value is 8.3 or since we round the numbers up it might go to 8.4 x will become 5

[Max@Math Revolution]

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In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 - x?

(1) If x is rounded to the nearest hundredth, then 10 - x = 8.56.

(2) If x is rounded to the nearest thousandth, then 10 - x = 8.564.

In the original condition there are 2 variables (a, b) thus we need 2 equations to match the number of variables. C is likely the answer. Solving the problem using (1) &(2), a=3, b=6 thus the answer is C. Remember to apply common mistake types in such integer problems. When we apply 'When it's easily C, consider A, B.' from common mistake types 4(A), and consider (1), we have variables with unknown values. In case of (2), a = 3, b =6 , therefore it is unique, and therefore the answer is B.


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